Evaluating Gene Flow Using Selected Markers: a Case Study

Evaluating Gene Flow Using Selected Markers: A Case Study

Thomas Lenormand, Thomas Guillemaud, Denis Bourguet1 and Michel Raymond

Laboratoire Ge´ne´tique et Environnement, Institut des Sciences de l’Evolution (UMR 5554), Universite´ Montpellier II, 34095 Montpellier Cedex 5, France Manuscript received September 16, 1997 Accepted for publication March 9, 1998

ABSTRACT The extent to which an organism is locally adapted in an environmental pocket depends on the selection intensities inside and outside the pocket, on migration, and on the size of the pocket. When two or more loci are involved in this local adaptation, measuring their frequency gradients and their linkage disequilbria allows one to disentangle the forces—migration and selection—acting on the system. We apply this method to the case of a local adaptation to organophosphate insecticides in the mosquito Culex pipiens pipiens in southern France. The study of two different resistance loci allowed us to estimate with support limits gene ﬂow as well as selection pressure on insecticide resistance and the ﬁtness costs associated with each locus. These estimates permit us to pinpoint the conditions for the maintenance of this pocket of adaptation as well as the effect of the interaction between the two resistance loci.

LTHOUGH evolutionary theory attempts mainly to this finite variance requires knowledge of population A explain past changes, its predictions can be tested sizes and of the patterns of isolation by distance (Rous- by examining actual evolutionary processes in natural set 1997). populations. To do so we must quantify the determinis- Another approach is to analyze directly the relative tic processes causing genetic evolution, namely, selec- magnitude of gene flow vs. selection through clinal pat- tion and gene flow, and take into account the unpredict- terns that have been extensively studied theoretically for able changes due to stochastic processes such as random various selection models (Felsenstein 1976; Endler drift and mutation. Among these factors only gene flow 1977). In an infinite environment and at equilibrium, (and stabilizing selection) will oppose genetic differenti- the cline slope is a robust estimate of the relative mag- ation between populations. Its evaluation is therefore nitude of selection vs. migration (Barton and Gale required for the understanding of the evolution of pop- 1993). Different methods can be used to infer the abso- ulations in their “adaptive landscape” (for review, see lute value of each term, and in all cases, they require Slatkin 1987). However, methods are lacking to evalu- extra information about the system such as (1) a direct ate gene flow independently of selection, mutation, or measure of dispersal, thus giving an indirect estimate drift. of selection (Endler 1977; Barton and Hewitt 1985); In most cases, it is possible to determine the relative (2) a genotypic parameter such as heterozygote defi- magnitude of gene flow vs. drift, and thus estimate the ciency at one locus or linkage disequilibria when several degree of isolation of populations. This determination loci are involved, the latter being more reliable (Mal- enables the evaluation of the effects of different kinds let and Barton 1989); (3) the variation of the cline of selection, of the geographic scale of a local adaptation through time, for instance, the speed of a wave of ad- (Nagylaki 1975), or whether such populations might vance of an advantageous gene (Fisher 1937) or the be able to cross an “adaptive valley” (Lande 1985). rate of modification of the cline shape when selection These methods, in principle, are valid for neutral and or migration is not constant. Despite their potential for independent genes at equilibrium and for a given rate the understanding of the evolution of populations over and mode of mutation. When averaged over many loci, their “adaptive landscape,” these methods have mainly these methods may be robust to slight departures from been used for the analysis of tension zones (Barton the assumptions (Slatkin and Barton 1989). However, 1982; Szymura and Barton 1986; Mallet et al. 1990; they provide an estimate of the number of “effective” Sites et al. 1995). The aim of this article is to show that migrants but not of migration variance (␴2). Estimating these methods can also be useful for understanding the dynamics of local adaptation. We have investigated the case of local adaptation of Corresponding author: Thomas Lenormand, Laboratoire Geńe´tique the mosquito Culex pipiens pipiens to organophosphate et Environnement, Institut des Sciences de l’Evolution (UMR 5554), insecticides in the Montpellier area in France. This ad- Universite´ Montpellier II, CC065 Place E. Bataillon, F-34095 Montpel- lier Cedex 5, France. E-mail: [email protected] aptation is conferred by resistance alleles at two major 1 Present address: Station de Recherche de lutte biologique, INRA La loci. Insecticide selection varies geographically, creating Minie`re, 78285 Guyancourt Cedex, France. a pocket of adaptation. We have analyzed clinal patterns

Genetics 149: 1383–1392 ( July 1998) 1384 T. Lenormand et al. at these two loci to estimate selection intensities and TABLE 1 gene flow. These estimates were used to evaluate the Nomenclature role of interaction between the two loci for the main- tainance of the pocket of adaptation. Finally, we com- Coding rules pared our estimates to direct or indirect estimates of selection intensity and gene flow in other studies. Genotype Genotype Phenotype Class Ester4 Ester4 (44) [4] {E} Ester4 Ester 0 (40) [4] {E} MATERIALS AND METHODS Ester 1 Ester 1 (11) [1] {E} Ester 1 Ester 0 (10) [1] {E} Culex pipiens and its environment: Larval development of 2 2 the mosquito C. p. pipiens takes place mainly in anthropic Ester Ester (22) [2] {E} 2 0 pools where insecticide control occurs. Females are presum- Ester Ester (20) [2] {E} ably fertilized at emergence (Weidhass et al. 1973) and then Ester4 Ester 1 (41) [41] {E} {eggs. Ester4 Ester 2 (42) [42] {E 200–150ف search for their blood meal and a site to lay Insecticides are applied during the breeding season, that is, Ester2 Ester 1 (21) [21] {E} approximately from April to October near Montpellier in Ester 0 Ester 0 (00) [0] {O} Chevillon southern France (see et al. 1995 fordetails) andare Ace.1R Ace.1R (RR) [RR] {R} restricted to a 20-km coastal belt. Between 1968 and 1990–91, Ace.1R Ace.1S (RS) [RS] {R} organophosphate (OP) insecticides were exclusively used for Ace.1RS Ace.1S (RSS) [RS] {R} mosquito control and have been replaced since then by the Ace.1RS Ace.1R (RSR) [RS] {R} Bacillus sphaericus toxin. However, in the Montpellier area, OP Ace.1RS Ace.1RS (RSRS) [RS] {R} insecticides are still used at large doses to control other Culic- S S ids and even to control C. p. pipiens in some situations (Anony- Ace.1 Ace.1 (SS) [SS] {S} mous 1990–1995). Additionally, residual doses of OP may be The resistance allele Ester 1 corresponds to overproduced of the order of lethal concentrations for susceptible mosqui- esterase A1, and alleles Ester 2 and Ester4 correspond to overpro- toes in many places of the treated area, possibly due to other S R. Eritja, duced esterases A2-B2 and A4-B4, respectively. Ace.1 codes pest controls ( personal communication). for a sensitive AChE1, Ace.1R for an insensitive AChE1, and Genetics of resistance: Two main loci are responsible for Ace.1RS for both acetylcholinesterases. “Coding rules” indicates OP resistance in C. p. pipiens. The first locus, Ace.1, codes for Bourguet the simplified code for each genotype, phenotype, and class an acetylcholinesterase (AChE1), the OP target ( corresponding to the genotype indicated in the first column. et al. 1996a; Malcolm et al. 1998) and has three alleles: Ace.1R S “Phenotype” corresponds to the electrophoretic phenotype that codes for an insensitive AChE1; Ace.1 that codes for a (Ester locus) or to the TPP phenotype (Ace.1 locus). “Class” sensitive AChE1; and Ace.1RS that corresponds to a duplication groups genotypes with at least one resistance allele. {E}/{O} of and codes for both enzymes (Raymond 1986; Ace.1 et al. for the presence/absence of at least one overproduced ester- Bourguet 1996b,c). The second locus corresponds to et al. ase and {R}/{S} for the presence/absence of at least one insen- a “super locus,” that is, two closely linked loci, and Est-3 sitive AChE1. Est-2, coding for esterases A and B, respectively (de Stordeur 1976; Pasteur et al. 1981a,b). Only 2 to 6 kb of DNA separate Est-3 from Est-2 (Rooker et al. 1996; Guillemaud et al. 1997). Resistance alleles at Est-3 and Est-2 induce an overproduction populations, resistance alleles at both loci are associated with of esterase, resulting in gene amplification or gene regulation fitness costs, in the absence of insecticides, through decreases (Rooker et al. 1996). Due to their close proximity, esterase in fecundity and adult survival and an increase in larval devel- genes are often coamplified as a single unit, which explains opmental time. These fitness costs tend to be higher for insen- the complete association of resistance alleles at both loci sitive acetylcholinesterase than for overproduced esterases (Rooker et al. 1996; Guillemaud et al. 1997). This coamplifi- (Chevillon et al. 1997). cation justifies considering them as a single “super locus,” Data collection: Pupae were sampled on July 5, 1995 in 10 which will hereafter be designated as Ester. In southern France, breeding sites along a 50-km north-south transect (Figure 1) three resistance alleles have been identified at this locus. Ester 1 across the treated and untreated areas studied by Guillemaud corresponds to an increased expression of the esterase A1, et al. (1998). They were reared until emergence, and adults whereas Ester 2 and Ester4 correspond to coamplification of es- were stored at Ϫ80Њ. terases A and B genes (A2-B2 and A4-B4, respectively). The For each mosquito, resistance alleles at the Ester and Ace.1 recombination rate between Ester and Ace.1 has been estimated loci were determined as follows. The thorax and the abdomen to be 14.5% (our unpublished results). The nomenclature were used to detect overproduced esterases using starch-gel used in this article is indicated in Table 1. electrophoresis (Tris-Maleate-EDTA 7.4 buffer; Pasteur et al. Fitness of resistant mosquitoes: The different resistance 1988). The head was used to characterize AChE1 using the alleles contribute unequally to OP resistance: in southern Te´moin-Propoxur-Propoxur (TPP) test described by Bour- France, insensitive acetylcholinesterase alleles confer in gen- guet et al. (1996e). Overproduced esterases are dominant eral a resistance higher than overproduced esterases (Ray- markers under our electrophoretic conditions, and the TPP mond et al. 1986; Poirie´ et al. 1992; Severini et al. 1993; test determines individuals displaying sensitive, resistant, or Raymond and Marquine 1994; Rivet et al. 1994). When over- both types of acetylcholinesterase. Thus, these methods do produced esterases and insensitive acetylcholinesterase are not allow complete genotype identification. Table 1 indicates present together in the same mosquito, the insecticide resis- the correspondence between each genotype and its simplified tance combines additively (Raymond et al. 1989). At both code (parentheses) as well as the corresponding identified loci, resistance alleles can be assumed to be codominant for phenotype [brackets]. In addition, a phenotypic class for indi- resistance (Raymond et al. 1987; Poirie´ 1991), although the viduals that carry at least oneresistance allele has been defined dominance of the resistance conferred by the Ace.1R allele is at each locus {braces}. To identify individuals at both loci, environment dependent (Bourguet et al. 1996d). In natural Ace.1 is indicated first, followed by Ester separated by a comma. Gene Flow in Culex pipiens 1385

can be very asymmetric. However, Nagylaki (1975, Equations 32–33) showed that they can be described by the maximum gene frequency and the gene frequency at the transition between the two environments and that the relative magnitude of selection vs. migration can be deduced from these charac- teristics. The full analytical treatment in the case of two loci in a semi-infinite environment has not been performed, although Slatkin (1975) worked out numerically the case of an infinite environment. When two loci with two alleles each are considered, fitness interactions between genes as well as their linkage must be considered. Additionally, linkage disequilibria are generated by migration that steepen each of the clines. Descriptive analysis: In order to test for the presence of frequency gradients at each resistance allele along the transect, data were fitted to descriptive cline models. Allelic distributions were fitted according to a scaled negative exponential. For instance, the frequencies of the four esterase alleles were modeled as follows: Ester 1: f1(x) ϭ h1.eϪa1.x2 Ester 2: f 2(x) ϭ h2.(1 Ϫ h1).eϪa2.x2 Ester 4: f4(x) ϭ h4.(1 Ϫ h1 Ϫ h2.(1 Ϫ h1)).eϪa4.x2 Ester 0: f0(x) ϭ 1 Ϫ f1(x) Ϫf2(x) Ϫ f4(x), where a1, a2, a4, h1, h2, and h4 are estimated parameters. The phenotypic distributions were computed by using these allelic distributions and by assuming each locus at Hardy- Weinberg equilibrium. The phenotype was considered to be a three-state or seven-state random variable for the Ace.1 and Ester locus, respectively (see Table 1). The likelihood of a sample was computed from the phenotypic multinomial distribution. Departure from Hardy-Weinberg proportions was tested in each population at the Ester locus by a likelihood ratio test. For an overall test, P values of each test were combined across populations using Fisher’s method (Manly 1985). At the Ace.1 Figure 1.—Samples location. The dashed line represents locus, departure from Hardy-Weinberg cannot be evaluated the limit between the treated and untreated area. because only three phenotypes are identified for three alleles. The presence of the Ace.1RS allele creates an apparent excess of [RS] when only the two alleles Ace.1R and Ace.1S are consid- Theoretical expectations: Let us consider first the case of ered. If Hardy-Weinberg proportions are assumed at this one locus. Let us note 1-si and 1-c, the probability that a locus, Ace.1RS frequencies can be computed from this appar- susceptible and a resistant homozygote survive exposure to ent excess of [RS], and an additional cline of allele frequency insecticide, and 1 and 1-c, the probability that they survive in can be fitted. the absence of insecticide. Further, si represents the fitness A linkage disequilibrium measure D ϭ freq{S,O} Ϫ freq{S} ϫ decrease due to insecticide exposure, and c the fitness cost of freq{O} was computed for each population and tested by an resistance. In the Montpellier area, insecticide treatments are exact test on the contingency table ({S},{R}) ϫ ({O},{E}) using restricted to the coastal belt (between 0 and L kilometers from the Genepop software (ver. 3.1a; Raymond and Rousset the sea). For one locus with two alleles, the fitness of each 1995). P values of each test were combined across populations genotype can be written as follows: using Fisher’s method. Simulations: In order to estimate migration and selection, resistant homozygotes: 1 ϩ sg(x) we used deterministic simulations to infer the allelic distribu- heterozygotes: 1 ϩ dsg(x) tion at equilibrium because the analytical solution is intracta- susceptible homozygotes: 1 Ϫ sg(x) ble andrequires the assumption of weak selection. One-dimension clines were simulated by a series of demes connected by s ϭ (si Ϫ c)/(2 Ϫ c Ϫ si) Mallet Barton  g(x) ϭ 1 for 0 р x Ͻ L migration as described in and (1989). The with  migration distribution was reflected at one edge of the step-  g(x) ϭϪ␣2 for x Ͼ L ping stone to simulate a semi-infinite environment. The proba- ␣2 ϭ c/s(2 Ϫ c), bility P of an individual in deme a migrating into deme a Ϫ where d is the dominance level (Ϫ1 Ͻ d Ͻ 1), x the distance t ϩ i was calculated using a symmetric binomial distribution from the coast, s the intensity of selection, and ␣2 the ratio B(2t, 1/2) corrected by the reflecting condition when a Ͻ t. of the selection coefficient for x Ͼ L and 0 Յ x Ͻ L. If 2(t Ϫ a) Ϫ i Ϫ 1 Ͼ 0, For codominance (d ϭ 0) and ␣ϭ1, Nagylaki (1975) showed that a cline may be maintained given that k Ͼ␲/4, 2t 2t then P ϭ (1/2)2t ϫ ϩ with k2 ϭ 2sL2/␴2 where ␴ is the standard deviation of parent- ΄΂ i ΃ ΂2(t Ϫ a) Ϫ i Ϫ 1΃΅ offspring distance measured along one dimension. Such clines 2t cannot be characterized only by their slope, in contrast to else P ϭ (1/2)2t ϫ . numerous other cases (Barton and Gale 1993), because they ΂ i ΃ 1386 T. Lenormand et al.

The migration variance was measured by ε2t/2, which is the variance of this distribution when a Ͼ t and where ε is the P distance betweendemes. Selection coefﬁcients were combined additively. The order of the processes was assumed to be repro- duction-migration-selection, as should be the case for C. pi- 0.02 1 0.4 1

piens. Ϫ Ϫ Migration and selection estimations: The method of estimation is based on the principle that all resistance allele frequencies should be clinal, decreasing from south to north (Figure 1). As a consequence, the mixing of genotypes by migration from populations along these clines should create heterozygote deﬁciencies at each locus (Wahlund effect) and positive linkage disequilibrium between loci. This disequilibrium is predicted to be maximal at a medium distance from the coast (x ≈ L) where the most dissimilar genotypes are mixed. Migra- tion and selection parameters were estimated conjointly such that the expected frequencies, computed using the simulation described above, and observed frequencies were as close as possible. We focused our study on the differences between susceptible and resistance alleles within and between loci rather than on the transient polymorphism or allele replacements at each locus. For such a purpose, we pooled individuals carrying at least one resistance allele at each locus. The phenotype was considered therefore to be a four-state ({S,O}, {S,E}, {R,O} and {R,E}; see Table 1) random variable, and the likelihood of a sample was computed from its multinomial distribution. Eleven parameters are needed to describe the system. Among them, three can be estimated from external data: the recombination rate (r ϭ 14.5%), the size of the treated area (L ϭ 20

km), and the epistasis for resistance (zero). Furthermore, we ), the frequencies of the different phenotypes (see Table 1 for nomenclature), assumed that epistasis for ﬁtness costs was negligible. These N value (using an exact test; see text).

estimations and assumptions allowed us to investigate the se- P lection intensities (sa, ␣a for the Ace.1 locus and se , ␣e , for the Ester locus) and the migration variance (␴2). To evaluate the influence of the dominance level on the estimation of the TABLE 2 migration variance, three cases of dominance for both loci were considered: recessivity (d ϭϪ1), codominance (d ϭ 0), and dominance (d ϭ 1). The influence of the recombination rate was also investigated for codominance at both loci. Model comparisons and tests: Maximum likelihood estimates (MLE) of parameters were computed conjointly using the Metropolis algorithm adapted from N. H. Barton (Szy- Phenotype frequencies along the transect mura and Barton 1986). G-tests were computed between related models and scaled to the dispersion of residual deviance (Crawley 1993). The support limits of a particular parameter were defined as the range of values within two units of log-likelihood from the maximum (Edwards 1972). [RR] [RS] [SS]

RESULTS Resistance allele frequencies and linkage disequilibria: The frequencies of the different phenotypes combined at both loci are given in Table 2. The Hardy- Weinberg expectation was not rejected at the Ester locus [0] [1] [2] [4] [41] [42] [21] [0] [1] [2] [4] [41] [42] [0] [1] [2] [4] [41] D(%) (global test over populations P ϭ 0.87). The linkage

disequilibrium estimates between Ester and Ace.1 (D) N and their corresponding P value are indicated in Table 2. A positive D is observed (Table 2, D Ͼ 0, combined test across populations P ϭ 5.10Ϫ5) that peaks (4–6%) near the ecotone transition, which is consistent with a linkage disequilibrium created by migration. Descriptive models: At the Ace.1 locus, a clinal pattern R RS is detected for both Ace.1 and Ace.1 alleles (Table 3). For each locality, distance is indicated from the coast in kilometers (km), the sample size ( LocalityPerolsMaurin km CournontSt. Gely 2.2 13Triadou 3.4 124Viols 186 0.07 21St. 91 Martin 0.04 25 0.04NotreDame 0.03 0.02St. 0.01 34 93 35 0.04 Bauzille 0.0 30 62Ganges 0.20 0.03 0.0 44 154 0.03 0.10 86 0.02 0.03 176 0.11 0.01 0.02 0.03 132 0.0 0.0 0.02 0.01 49 0.0 0.01 0.0 0.02 0.0 0.01 0.0 0.04 0.0 0.0 0.0 0.06 0.0 0.0 89 0.01 0.0 0.09 0.0 0.0 0.0 0.02 0.0 0.0 0.0 0.0 0.06 0.15 0.02 0.0 0.0 0.14 0.02 0.01 0.06 0.0 0.0 0.0 0.0 0.08 0.33 0.0 0.0 0.0 0.0 0.0 0.0 0.23 0.01 0.10 0.0 0.0 0.48 0.0 0.16 0.10 0.0 0.33 0.01 0.0 0.01 0.06 0.09 0.0 0.09 0.29 0.0 0.01 0.0 0.23 0.20 0.0 0.01 0.02 0.02 0.01 0.26 0.23 0.03 0.02 0.0 0.01 0.0 0.04 0.31 0.0 0.02 0.01 0.0 0.0 0.0 0.03 0.0 0.0 0.0 0.18 0.01 0.0 0.14 0.19 0.0 0.0 0.14 0.01 0.0 0.16 0.18 0.01 0.0 0.01 0.04 0.01 0.01 0.02 0.01 0.0 0.19 0.0 0.0 0.01 0.4 0.0 0.01 0.0 0.35 0.05 0.01 0.36 0.02 0.43 0.45 0.04 0.39 0.0 1.5 0.10 0.03 0.0 0.0 0.05 0.0 0.0 0.45 0.11 0.02 0.09 0.0 0.0 0.0 0.0 0.14 0.0 5.5 0.13 0.02 0.12 0.56 0.01 0.024 4.1 0.0 0.01 5.1 3.8 0.097 0.0 1.8 0.01 0.046 6.3 0.21 0.46 0.018 0.0 The presence at high frequencies of the duplication and the value of the estimated linkage disequilibrium D (in percent) and its associated Gene Flow in Culex pipiens 1387

TABLE 3 1975 and Figure 2a), but is shifted 8 km into the un- Descriptive fit tests treated area. Effect of the linkage: As in the case of a single locus, Locus Model Deviance %TD Scaled G-test the ratio of selection intensities in treated and untreated areas (␣2) and the selection-migration ratio (k) depend Ester a1, a2, a4 71.90 0.77 — only on the relative magnitude of selection vs. gene flow a1 ϭ 0, a2, a4 132.64 0.58 Ͻ0.00001 a1, a2 ϭ 0, a4 78.20 0.75 0.012 for each locus (data not shown). However, the linkage a1, a2, a4 ϭ 0 211.11 0.32 Ͻ0.00001 between the two loci (14.5%) has a noticeable effect Ace.1 aR, aRS 55.65 0.88 — on the Ester locus: in order to maintain the Ester cline aR ϭ 0, aRS 189.66 0.58 Ͻ0.00001 at the same frequency in the absence of selection on aR, aRS ϭ 0 74.91 0.83 0.017 Ace.1, selection (or k2) would have to be 26% higher. In contrast, to maintain the Ace.1 cline at the same For each allele, the presence of a cline was tested using the 2 descriptive models described in the text. “Model” indicates level, k need only be increased by 7% in the absence the fitted parameters. At the Ester locus, parameters a1, a2, of selection on the Ester locus. and a4 correspond to the Ester 1, Ester 2, and Ester4 alleles, respec- Dominance effect: The different hypotheses of domi- tively. At the Ace.1 locus, aR and aRS refer to the Ace.1R and nance do not have an important effect neither on the RS Ace.1 alleles, respectively. “%TD” indicates the percent of estimation of migration variance (␴ range 6.6–7.1) nor the total deviance explained by the model. The P value of the scaled G-test is indicated in the last column. on its support limits (Table 5). In fact, for given frequency gradients, the estimation depends mainly on the linkage disequilibrium pattern, as previously pointed (0.33 on the coast, Table 4) is thus strongly supported, out by Barton (1982). and its cline explains well the pattern of apparent excess Recombination effect: The estimate of the migration of heterozygotes in the transect. These two similar clines variance strongly depends on the recombination rate explain 88% of the total deviance at Ace.1 locus. How- between Ace.1 and Ester: for the same migration variance, ever, the frequency of the duplicated allele Ace.1RS is the closer the loci the higher the linkage disequilib- underestimated by assuming Hardy-Weinberg propor- rium. The recombination rate (r) of 14.5% was esti- tions because a heterozygote deficiency due to migra- mated between Ester and Ace.1 based on 503 indi- tion is expected. At the Ester locus, the model explains viduals (T. Lenormand, T. Guillemaud, D. Bourquet 77% of the total deviance. Significant and similar clinal and M. Raymond, unpublished results). Figure 3 shows patterns were found for all esterase resistance alleles, the joint support area for r and ␴, assuming codomi- even for Ester 2, which is rare (Tables 3 and 4). These nance at both loci. Support limits of ␴ are not affected results are consistent with the hypothesis that, for each by error measurements on the recombination rate (see locus, the selection pressures acting on resistance alleles Figure 3). are similar, that is, that the main differences in selection Selection intensities: Estimations of selection intensities pressure are between susceptible and resistance alleles. may not be as robust as the estimation of ␴, because Migration-selection models: The migration-selection they depend on the assumptions of dominance. How- models explain 92–93% of the total deviance (Table 5 ever, the different cases of dominance that were investi- and Figure 2). The maximum likelihood estimate of the gated are not equally likely (Table 5). In particular, parent-offspring standard deviation measured on one models considering dominance at Ace locus (models times less likely than those 20ف dimension is ␴ϭ6.6 km.genϪ1/2 (support limits 4.8–8.7 A–C in Table 5) are km.genϪ1/2) when codominance is assumed at both loci. that consider recessivity (models G–I). In contrast, for It should be underlined that the expected linkage dis- a given dominance on the Ace.1 locus, there are no equilibrium does not peak at the ecotone transition, as noticeable differences between models considering dif- in the case of an infinite environment (see Slatkin ferent dominance levels on the Ester locus. When consid-

TABLE 4 Descriptive ﬁt estimates

Clines a SL f(0) SL Ester 1 9.87 ϫ 10Ϫ4 7.75 ϫ 10Ϫ4–1.23 ϫ 10Ϫ3 0.123 0.105–0.144 Ester 2 9.52 ϫ 10Ϫ4 3.75 ϫ 10Ϫ4–1.75 ϫ 10Ϫ3 0.014 0.008–0.021 Ester4 6.62 ϫ 10Ϫ4 5.75 ϫ 10Ϫ4–7.6 ϫ 10Ϫ4 0.430 0.40–0.46 Ace.1R 5.7 ϫ 10Ϫ4 5.0 ϫ 10Ϫ4–6.9 ϫ 10Ϫ4 0.489 0.46–0.515 Ace.1RS 3.0 ϫ 10Ϫ3 2.0 ϫ 10Ϫ4–5.1 ϫ 10Ϫ3 0.338 0.29–0.389 Estimated parameters for each allelic cline, where the gene frequency is a function of distance to the sea f(x) ϭ f(0)eϪax2, with f(0) being the maximum frequency. “SL” indicates the support limits. 1388 T. Lenormand et al.

TABLE 5 Selection-migration models: different cases of dominance

2 2 Model da de ␴ SL sa se ␣a ␣e Deviance (%TD) A 1 1 6.9 5.0–9.4 0.2 0.067 0.2 0.32 41.0 (91.8) B 1 0 7 5.0–9.2 0.2 0.064 0.21 0.52 40.2 (92.0) C1Ϫ1 7.1 5.2–9.4 0.2 0.08 0.22 1.47 37.7 (92.5) D 0 1 6.7 4.9–8.9 0.13 0.056 0.45 0.35 38.0 (92.4) E 0 0 6.6 4.8–8.7 0.125 0.055 0.46 0.59 37.0 (92.7) F0Ϫ1 6.8 4.9–9.0 0.13 0.062 0.49 1.58 37.5 (92.6) G Ϫ1 1 6.8 4.9–9.2 0.12 0.054 1.16 0.38 33.3 (93.4) H Ϫ1 0 6.7 4.8–8.9 0.11 0.05 1.21 0.65 33.3 (93.4) I Ϫ1 Ϫ1 6.6 4.7–8.8 0.11 0.051 1.25 1.77 33.4 (93.4)

Three cases of dominance were considered at each locus. da and de are the dominance cases associated with the Ace.1 and Ester loci, respectively. The MLE and the support limits (SL)of␴is indicated in each case, as 2 2 well as the MLE of selection intensity (sa and se) and selection ratio (␣a and ␣e ) associated with each locus. The residual deviance of each model and the percent of total deviance explained by each model (%TD) are indicated in the last columns. ering only the most likely models (E–I), selection inten- External estimation of parameters: We supposed that the on summer clines were observed at migration-selection 0.055ف on Ace.1 (sa) and 0.12ف sity is likely to be

Ester (se). For codominance at both loci (model E), these equilibrium. This is of course not exactly true, because selection intensities give an estimate of the insecticide selection intensities vary during the year. However, the selection pressure (si ≈ 0.30 for Ace.1 and ≈0.16 for high selection pressure and migration variance esti- Ester) and of the intensities of the fitness costs (c ≈ 0.11 mated are consistent with very rapid adjustments of fre- and ≈0.06 for Ace.1 and Ester, respectively). quencies. Moreover, frequencies, as well as selection intensities, are autocorrelated in time: adjustments to selection intensities require only limited changes in fre- DISCUSSION quency. Validity of the assumptions: The analysis of clinal We assumed a symmetric binomial migration distribu- patterns allowed us to infer in a single step the different tion with a reflecting condition on the sea coast. Depar- parameters that are relevant to describe the dynamics tures from this assumption could exist due to several of local adaptation, i.e., gene flow and selection coeffi- factors. First, the migration distribution may be more cients in the different part of the environment for each leptokurtic. This may not strongly affect the peak of locus. Additionally, the model developed permits us to linkage disequilibrium at the ecotone transition (see explain 92% of the total deviance of the data in a quite Mallet et al. 1990), but further work is required to economical manner. However, many simplifications settle this issue. Second, it is possible that density varia- were assumed, and external estimations were used for tions may cause asymmetric flux of migrants. These some parameters. We will discuss these points in turn. variations in density may be caused by the control of Models of selection: We assumed that the different resis- mosquito populations in the treated area, which affects tance alleles at each locus were subjected to the same population sizes. However, the number of favorable lar- selection pressure. This is probably not true since allele val breeding sites varies as well and would tend to com- replacements were observed over the last 20 years (Guil- pensate for this effect: the density of C. p. pipiens larval lemaud et al. 1998). However, the rate of these replace- sites are associated with human activity, which is more ments is quite low, at least for the Ester locus, and can important in the treated (urban and peri-urban areas) be explained by fitness differences between resistance than in the untreated areas (countryside). Third, be- alleles that are much lower (1–2%) than those between cause the density of hosts (for blood feeding) and of resistance and susceptible alleles (Guillemaud et al. larval sites is likely to vary along the transect, the hypoth- 1998). Additionally, the fitted selection intensities may esis of a constant migration variance may be violated if mainly represent those associated with the most com- most of the migration variance is due to foraging behav- mon alleles. This is especially true for the Ester locus: ior (search for a blood meal and a site to lay eggs; among individuals that carry at least one resistance al- Reisen et al. 1991). Fourth, the pattern of cytoplasmic lele, only 15% lack the Ester4 allele. The situation may incompatibilities caused by Wolbachia endosymbionts not be as clear for the Ace.1 locus, where both the Ace.1R may cause local variation of the effective migration vari- and the duplicate Ace.1RS alleles are present in non- ance (Magnin et al. 1987). For these reasons, the effec- negligible frequencies and where the rate of allele re- tive migration estimated in the Montpellier area may placement over time is not documented. not be considered as a general feature of the species. Gene Flow in Culex pipiens 1389

Figure 3.—Maximum likelihood estimates (bold line) of the standard deviation of parent-offspring distance (␴ in km·genϪ1/2) as a function of the recombination rate (r) between the Ace.1 and Ester loci. Outer lines correspond to the support limits of ␴. The small circle is the joint maximum likelihood of r and ␴, and the dashed ellipse the joint support area for both r and ␴.

quinquefasciatus. Over a period of 12 days, Reisen et al. report an mdt between 0.6 and 1 km (1991) or 2 km (1992) for C. p. quinquefasciatus (which are both strongly biased; see above), and O’Donnell et al. (1992) estimated an mdt of 6.8 km for C. annulirostris. Given an average of 8–10 days from adult emergence to the first oviposition (Lowe et al. 1973; Smittle et al. 1973; Weid- haas et al. 1973), these estimates are in agreement with ours (6.6 km·genϪ1/2 corresponds to an mdt of 0.66–0.82 km/day), although it appears that mark-recapture experiments should be performed on a larger scale to give more reliable estimates of dispersal for Culex species. Migration-drift equilibrium: The relative magnitude of Figure gene flow vs. drift has been evaluated in southern France 2.—Fitted and observed clines and linkage disequi- Chevillon librium. (a) Linkage disequilibrium D (see text); (b) {S,O} by et al. (1995), using allozymic markers. frequency; (c) {R,O} frequency; (d) {S,E} frequency; (e) {R,E} Their study supports the hypothesis that migration out- frequency. Circles represent observed values and lines fitted weighs drift in C. p. pipiens populations, which is in good values for codominance at both loci (see text). agreement with our high estimate of migration variance. However, our estimate of ␴ allows us to disentangle drift and migration and to estimate average effective Comparison with other estimates: Direct measures of population densities. We reanalyzed the allozymic data dispersal: Many studies have investigated the active dis- from Chevillon et al. (1995), using the method de- persal of Culex species by mark-recapture experiments. scribed in Rousset (1997). Samples were collected in Although none consider C. p. pipiens, plenty of data is 31 localities distributed along the Mediterranean coast available for C. p. quinquefasciatus, the tropical subspe- (southern France and northern Spain) and analyzed at Mattingly cies of C. pipiens ( et al. 1951), and other five loci. A regression ofFST/(1ϪFST) estimates computed Culex species. These dispersal estimations are often bi- for pairs of subpopulations on the logarithm of geo- ased toward low values either as a consequence of the graphical distance was performed using the Genepop small areas investigated (4 km, Morris et al. 1991; Rei- software (ver. 3.1a; Raymond and Rousset 1995). A sen et al. 1991; 1.5 km, Schreiber et al. 1988) or of the significant isolation by distance was detected (Mantel absence of correction for dilution of sampling effort test, P ϭ 0.0123). The slope of this regression was used with distance (Reisen et al. 1991, 1992). In all these to estimate 1/(4 De.␲␴2), where De is the density of studies, some individuals were trapped close to the limit mosquitoes (Rousset 1997). The estimate of De.␴2 is of the trapping grid. Morris et al. (1991) report a mean 16.3 individuals. Using our estimate of ␴ϭ6.6 distance traveled (mdt) per day for three Culex species km·genϪ1/2, the estimate of the density De is 0.37 individ- (0.73, 0.76, and 0.84 km for C. erraticus, C. nigripalpus, uals per km2. This result is surprising when compared and C. salinarius, respectively), and Schreiber et al. to the mosquito densities observed in the field during (1988) report a mdt of 1.27 km after 36 hr for C. p. the breeding season (104–107 individuals/km2; Reisen 1390 T. Lenormand et al. et al. 1991, 1992; Lindquist et al. 1967). This strongly mating gene flow from selected loci, the selection pres- suggests that mosquito populations are heterogeneous sure is taken explicitly into account. This situation pres- in space, that they vary seasonally, and that they endure ents different advantages. First, there is no need to severe bottlenecks. A simple explanation of these results formulate ad hoc hypotheses concerning neutrality of would be the low density of the founders in early spring. markers; second, few markers are needed; and third, High mortality rates during overwintering (up to 80– predictable frequency patterns are expected and can 90%; Minar and Ryba 1971; Sulaiman and Service be tested. However, this method requires that some 1983) and between pupation and oviposition (90%; genes be identified that are subjected to clear selection Lowe et al. 1973; Weidhaas et al. 1973) have been re- pressures and that some conclusion be made a priori ported, and weather-related mortality is likely to occur concerning these selection pressures. Additionally, this in the spring due to a fall of temperature after warming method permits working at a restricted scale in time periods. Finally, it is also possible that the De estimate and space where assumptions of constant population is not totally accurate due to the different scales of the sizes and homogeneity of space are the most reliable. two approaches. In particular, it is possible to take explicitly into account Selection intensities: We found that insecticide selection specific features of the environment (e.g., presence of on Ace.1 locus (si ≈ 0.30) was higher than on Ester locus geographic barriers), if needed. The drawback is that (si ≈ 0.16). This is consistent with the resistance ratio such estimates can hardly be representative of other associated with these loci: the insensitive AChE1 confers environmental conditions because they are not aver- a higher level of resistance. However, even if selection aged over a long period of time and over large geo- has been clearly associated with OP insecticides, it has graphic areas. However, they provide an “instantaneous” never been measured in natural populations. The evalu- measure of dispersal that is the most pertinent for the ation of fitness costs is even less straightforward because area, the period, and the scale considered, especially in all fitness components can be influenced during both the case of recent local adaptation. In this respect, these larval and adult stages. For example, larval development measures may be comparable to mark-recapture esti- time, fecundity, susceptibility to parasites or predators, mates. However, direct measures of dispersal do not ability to blood feed, etc., can be modified by the pres- provide estimates of effective gene flow and may miss ence of resistance genes (e.g., Wood and Bishop 1981; long-distance migrants because individuals are often Roush and McKenzie 1987). For C. p. pipiens, some trapped at the limit of the trapping grid. fitness costs on larval development time and female We have estimated gene flow using two selected ge- fecundity have been experimentally found in natural netic markers. This estimation is an essential step in populations (Bourguet 1996). The presence of the understanding the dynamics of selected genes when Ace.1R allele increased the generation time by 4.3%. In selection pressures vary in space and time. We have an exponential growth phase of the population (during focused on the selection-migration equilibrium on a the spring), this difference gives an estimation of fitness local scale, considering gene flow as a “constraining cost (c) between 0.07 and 0.13 for an effective fecundity force” reducing the potential for local adaptation. How- between five and 25 offspring. This estimation may be ever, on a much wider scale, gene flow is also responsible conservative, because only larval development time is for the spread of resistance alleles across the species taken into account and indicates that our estimates are range mainly by passive migration (Qiao and Raymond not overestimated (c ≈ 0.11 and 0.06 for Ace.1 and Ester, 1995; Guillemaud et al. 1996 and reference therein). respectively). At these two scales, gene flow may not be comparable, Conditions for the maintenance of Ace.1 and Ester playing either a conservative or a creative role. clines: Both clines maintain each other. Their concomi- We are very grateful to C. Chevillon, N. Pasteur, F. Rousset tant presence makes the conditions for their mainte- and J. Britton-Davidian for their helpful comments and discussion nance less strict than if they were alone. However, this about the manuscript. This work was financed by Groupement de effect concerns mainly the least selected locus, Ester. We Recherche 1105 du programme Environnement, Vie et Socie´te´sdu computed that the frequencies of Ester 0 and Ace.1S in Centre National de la Recherche Scientifique, the Re´gion Languedoc- Roussillon (no. 963223) and ACC SV3 (no. 9503037). T.L. was sup- coastal populations would be 0.074 and 0.013 higher, ported by an ASC from Institut National de la Recherche Agronom- respectively, if each locus was considered independently ique. Contribution 98.062 of the Institut des Sciences de l’Evolution from the other. Using the estimates of migration and de Montpellier (UMR CNRS 5554). selection provided by model E (codominance at both loci), the Ester cline would disappear if the width of the treated area (L) was reduced to 11 km. Similarly, the LITERATURE CITED Ace.1 cline is not maintained when L Ͻ 7 km. In an Anonymous, 1990–1995 Rapport d’activite´ technique et scienti- infinite and uniform environment, the minimum size fique. Entente Interde´partementale pour la De´moustication du .Littoral Me´diterraneén, Montpellier, France 15ف of a potential adaptive pocket would therefore be Barton, N. H., 1982 The structure of the hybrid zone in Uroderma km for codominance at both loci. bilobatum (Chiroptera: Phyllostomatidae). Evolution 36: 863–866. Estimating gene flow from selected loci: When esti- Barton, N. H., and K. S. Gale, 1993 Genetic analysis of hybrid Gene Flow in Culex pipiens 1391

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